Titration of NaOH and HCl need help

How to answer the question: why the pink colour (from 2-3 phenolphthalein indicator) obtained at the end point of the titration in this experiment gradually disappears over time?
Is it because of that the water will reverse back to the form of H+ and OH-?

Hello, I think phenolphthalein begins to decompose with increasing hydrolysis over time. The quinoid form is pinky-purple, but with increasing hydrolysis, acidic products develop and as cronxeh said, the pH is lowered. It is very likely that the carbon dioxide in the medium causes the pH drop, as it gives carbonic acid with water.

It depends on which way the reaction went - either increasing in pH (from 8.2 to 10 - becoming red colour) or decreasing in ph (becoming acidic and dropping from 8.2 down - colorless)

So in your case you are asked (probably) to add phenolphtalein into HCl, and then gradually make drops of NaOH while stirring it.

What happens is that phenolphtalein is colorless at first (becomes the environment is acidic - HCl), and stirring the mixture while neutralizing it (adding NaOH) insures that you dont get fooled by forming pink bubbles at individual spots

What happens next is out of my realm but I'm going to imagine here, so bear with me:
phenolphtalein + HCl --> HC2H3O2 (phenolphtalein added to HCl, the pH is less than 8.2 - its colorless)

You titrating (neutralizing):
HC2H3O2 + NaOH --> Na(C2H3O2) + H2O (the pH raises around 8.2 to 10 depending on how vigorously you titrate)

Now during this titration reaction the electrons are free to move between phenolphtalein-HCl juncture and if you stop titrating the color will disappear and pH would drop into acidic range

AFAIK if you titrate fully and reaction is complete the color will stay pink/red depending how much NaOH u added

Phenolthalein does NOT decompose at its endpoint pH.
Phenolthalein does NOT re-equilibrate to produce an acidic product at its endpoint pH.

Slightly basic solutions DO absorb CO2 from the air and produce the weak acid HCOOOH. The absorption happens fairly slowly and a faint pink endpoint will gradually fade. Adding more NaOH after the faint endpoint is reached (producing a darker endpoint) will cause the pink solution to persist much longer but also results in an inaccurate titration and should be avoided. When I'm grading a student's lab technique score, these dark endpoints are a guaranteed low score!